Question

Given $\triangle RST \cong \triangle XYZ$. Points $P$ and $W$ lie on $ST$ and $YZ$, respectively. Which of the following statements are true?
A) If $P$ is the midpoint of $\overline {ST}$ and $W$ is the midpoint of $\overline {YZ},$ then $\triangle RSP\cong \triangle XYW$.

B) If $\overline {RP}$ bisects $\angle SRT and [tex] \overline {XW}$ bisects $\angle YXZ$, then $\triangle RSP\cong \triangle XYW$.

C) If $RP=XW$, then $\triangle RSP\cong \triangle XYW$.

D) If $\overline {RP}\perp\overline {ST}$ and $\overline {XW}\perp\overline{YZ}$, then $\triangle RSP\cong \triangle XYW$.